A parameterization of heat and momentum fluxes in ... - LPAS - EPFL

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In Fig. 1 a vertical profile of the ratio between the local u * (defined as u*( z) = uw() z + vw() z 2 2 ) and the mean horizontal wind computed by the model at different hours in the centre of the urban area is presented A plot of the same variable measured for a series of field studies (from Roth, 2000) is in Fig. 2. The magnitude of the calculated values is comparable with the measurements and also the profiles have the same behaviour above the roof level. It is interesting to note, also, that below roof level, there is a decrease of this ratio in connection with the decrease of the Reynolds Stress as it was measured, for example, by Rotach 1993 in Zurich (not shown). Figure 2: Vertical profiles of the ratio between local ustar and horizontal mean wind for different ‘urban’ dataset. From Roth, 2000.. During day and night, walls have the biggest impact on the sink of momentum. The vertical section of the horizontal wind speed (Fig. 3) shows a deceleration of the flow over the urban areas, close to the surface, and acceleration above, due to the heat island effects. During night, the effects of the town are a reduction of the wind speed. Both phenomena are ‘qualitatively’ in agreement with many observations recorded in urban areas.
Figure 3: Vertical section of the east-west component (parallel to the plane) of the mean wind at noon (left) and midnight (right). The thick line on the x-axis represent the urban area. 3.2 Energy The energy equation is modified in the following way ∂ρθ ∂ρθUi ∂ρϑui =− − + H + H + H ∂t ∂x ∂x i i W S R As it is done for momentum it is possible to compute a value for ϑ * for the street. H ⎡ S ⎤ S =−ρu ϑ ⎢ ⎣V −V ⎥ b ⎦ S * S * S and this is applied only at surface level. From the value ofϑ * computed for the roof H =−ρu R * R * R ⎡SR ⎤ ϑ ⎣ ⎢ V ⎦ ⎥ this modification is applied at roof level. For the heat fluxes from the walls the formulation from Clarke, 1985 was used. H w hc⋅( θ air −θ wall ) = C with ⎛ ⎛ hc = 5. 678⋅ ⎜109 . + 0. 23⋅⎜ ⎜ ⎜ ⎝ ⎝ p U x + U 2 2 0. 3048 and C p is the specific heat of the air. y ⎞⎞ ⎟⎟ ⎟⎟ ⎠⎠
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A parameterization of heat and momentum fluxes in ... - LPAS - EPFL

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